Abstract: We present a detailed analysis of classical solutions in the bosonic sectorof the electroweak theory which describe vortices carrying a constant electriccurrent ${\cal I}$. These vortices exist for any value of the Higgs boson massand for any weak mixing angle, and in the zero current limit they reduce to Zstrings. Their current is produced by the condensate of vector W bosons andtypically it can attain billions of Amperes. For large ${\cal I}$ the vorticesshow a compact condensate core of size $\sim 1-{\cal I}$, embedded into aregion of size $\sim{\cal I}$ where the electroweak gauge symmetry iscompletely restored, followed by a transition zone where the Higgs fieldinterpolates between the symmetric and broken phases. Outside this zone thefields are the same as for the ordinary electric wire. An asymptoticapproximation of the large ${\cal I}$ solutions suggests that the current canbe {arbitrarily} large, due to the scale invariance of the vector bosoncondensate. Finite vortex segments whose length grows with ${\cal I}$ seem tobe perturbatively stable. This suggests that they can transfer electric chargebetween different regions of space, similarly to thunderbolts. It is alsopossible that they can form loops stabilized by the centrifugal force -electroweak vortons.